Epsilon irreflexivity of ordinals: no ordinal class is a member of
itself. Theorem 2.2(i) of [BellMachover] p. 469, generalized to
classes.
We prove this without invoking the Axiom of Regularity. (Contributed by
NM, 2-Jan-1994.)

A way to show that an ordinal number equals the minimum of a collection
of ordinal numbers: it must be in the collection, and it must not be
larger than any member of the collection. (Contributed by NM,
14-Nov-2003.)

Obsolete proof of suctr4473 as of 5-Apr-2016. The successor of a
transitive set is transitive. (Contributed by Scott Fenton,
21-Feb-2011.) (Proof modification is discouraged.)
(New usage is discouraged.)